Question

derive the eq maximum motion
of circular motion of a car in banked road​

Answer 1

N is normal force,

f is frictional force

Ncosθ=mg+fsinθ⟶(1)

and

fcosθ+Nsinθ=

r

mv

2

​

⟶(2)

f=μN⟶(3)

∴Ncosθ=μNsinθ+mg

N(cosθ−μsinθ)=mg

⇒N=

cosθ−μsinθ

mg

​

⟶(4)

Putting (3) and (4) in (2):

cosθ−μsinθ

μmgcosθ

​

+

cosθ−μsinθ

mgsinθ

​

=

r

mv

2

​

⇒μmgrcosθ+mgrsinθ=mv

2

cosθ−μmv

2

sinθ

⇒μmgr+mgrtanθ=mv

2

−μmv

2

tanθ

⇒mgr(μ+tanθ)=mv

2

(1−μtanθ)

⇒

(1−μtanθ)

rg(μ+tanθ)

​

=v

2

⇒v=

(1−μtanθ)

rg(μ+tanθ)

​

​